Efficient quantum algorithms for some instances of the semidirect discrete logarithm problem. (arXiv:2312.14028v1 [cs.CR])

The semidirect discrete logarithm problem (SDLP) is the following analogue of
the standard discrete logarithm problem in the semidirect product semigroup
$G\rtimes \mathrm{End}(G)$ for a finite semigroup $G$. Given $g\in G, \sigma\in
\mathrm{End}(G)$, and $h=\prod_{i=0}^{t-1}\sigma^i(g)$ for some integer $t$,
the SDLP$(G,\sigma)$, for $g$ and $h$, asks to determine $t$. As Shor's
algorithm crucially depends on commutativity, it is believed not to be
applicable to the SDLP. Previously, the best known algorithm for the SDLP was
based on Kuperberg's subexponential time …

algorithms end integer problem product quantum quantum algorithms sigma standard